High-accuracy quasi-variable mesh method for the system of 1D quasi-linear parabolic partial differential equations based on off-step spline in compression approximations
Abstract In this article, we propose a new two-level implicit method of accuracy two in time and three in space based on spline in compression approximations using two off-step points and a central point on a quasi-variable mesh for the numerical solution of the system of 1D quasi-linear parabolic p...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2017-08-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-017-1274-3 |
| _version_ | 1811214437280907264 |
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| author | RK Mohanty Sachin Sharma |
| author_facet | RK Mohanty Sachin Sharma |
| author_sort | RK Mohanty |
| collection | DOAJ |
| description | Abstract In this article, we propose a new two-level implicit method of accuracy two in time and three in space based on spline in compression approximations using two off-step points and a central point on a quasi-variable mesh for the numerical solution of the system of 1D quasi-linear parabolic partial differential equations. The new method is derived directly from the continuity condition of the first-order derivative of the spline function. The stability analysis for a model problem is discussed. The method is directly applicable to problems in polar systems. To demonstrate the strength and utility of the proposed method, we solve the generalized Burgers-Fisher equation, generalized Burgers-Huxley equation, coupled Burgers-equations and heat equation in polar coordinates. We demonstrate that the proposed method enables us to obtain high accurate solution for high Reynolds number. |
| first_indexed | 2024-04-12T06:03:22Z |
| format | Article |
| id | doaj.art-ffebe5aba7824c5d9ad8dd254ac27081 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-04-12T06:03:22Z |
| publishDate | 2017-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-ffebe5aba7824c5d9ad8dd254ac270812022-12-22T03:44:58ZengSpringerOpenAdvances in Difference Equations1687-18472017-08-012017113010.1186/s13662-017-1274-3High-accuracy quasi-variable mesh method for the system of 1D quasi-linear parabolic partial differential equations based on off-step spline in compression approximationsRK Mohanty0Sachin Sharma1Department of Applied Mathematics, South Asian UniversityDepartment of Mathematics, Faculty of Mathematical Sciences, University of DelhiAbstract In this article, we propose a new two-level implicit method of accuracy two in time and three in space based on spline in compression approximations using two off-step points and a central point on a quasi-variable mesh for the numerical solution of the system of 1D quasi-linear parabolic partial differential equations. The new method is derived directly from the continuity condition of the first-order derivative of the spline function. The stability analysis for a model problem is discussed. The method is directly applicable to problems in polar systems. To demonstrate the strength and utility of the proposed method, we solve the generalized Burgers-Fisher equation, generalized Burgers-Huxley equation, coupled Burgers-equations and heat equation in polar coordinates. We demonstrate that the proposed method enables us to obtain high accurate solution for high Reynolds number.http://link.springer.com/article/10.1186/s13662-017-1274-3quasi-linear parabolic equationsquasi-variable meshspline in compressiongeneralized Burgers-Fisher equationscoupled Burgers equationNewton’s iterative method |
| spellingShingle | RK Mohanty Sachin Sharma High-accuracy quasi-variable mesh method for the system of 1D quasi-linear parabolic partial differential equations based on off-step spline in compression approximations Advances in Difference Equations quasi-linear parabolic equations quasi-variable mesh spline in compression generalized Burgers-Fisher equations coupled Burgers equation Newton’s iterative method |
| title | High-accuracy quasi-variable mesh method for the system of 1D quasi-linear parabolic partial differential equations based on off-step spline in compression approximations |
| title_full | High-accuracy quasi-variable mesh method for the system of 1D quasi-linear parabolic partial differential equations based on off-step spline in compression approximations |
| title_fullStr | High-accuracy quasi-variable mesh method for the system of 1D quasi-linear parabolic partial differential equations based on off-step spline in compression approximations |
| title_full_unstemmed | High-accuracy quasi-variable mesh method for the system of 1D quasi-linear parabolic partial differential equations based on off-step spline in compression approximations |
| title_short | High-accuracy quasi-variable mesh method for the system of 1D quasi-linear parabolic partial differential equations based on off-step spline in compression approximations |
| title_sort | high accuracy quasi variable mesh method for the system of 1d quasi linear parabolic partial differential equations based on off step spline in compression approximations |
| topic | quasi-linear parabolic equations quasi-variable mesh spline in compression generalized Burgers-Fisher equations coupled Burgers equation Newton’s iterative method |
| url | http://link.springer.com/article/10.1186/s13662-017-1274-3 |
| work_keys_str_mv | AT rkmohanty highaccuracyquasivariablemeshmethodforthesystemof1dquasilinearparabolicpartialdifferentialequationsbasedonoffstepsplineincompressionapproximations AT sachinsharma highaccuracyquasivariablemeshmethodforthesystemof1dquasilinearparabolicpartialdifferentialequationsbasedonoffstepsplineincompressionapproximations |